%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM924+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:17:31 PM UTC 2026
% Result : Theorem 2.64s 1.37s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
fof(f43,axiom,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
fof(f62,axiom,
! [X0] : number_number_of(int,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
fof(f63,axiom,
! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
fof(f102,axiom,
! [X0] : times_times(int,pls,X0) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
fof(f136,axiom,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_zadd__commute) ).
fof(f137,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_zero__is__num__zero) ).
fof(f155,conjecture,
ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f156,negated_conjecture,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
inference(negated_conjecture,[status(cth)],[f155]) ).
fof(f157,plain,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
inference(flattening,[],[f156]) ).
fof(f207,plain,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
inference(cnf_transformation,[],[f157]) ).
fof(f243,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(cnf_transformation,[],[f43]) ).
fof(f257,plain,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
inference(cnf_transformation,[],[f136]) ).
fof(f262,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f137]) ).
fof(f282,plain,
! [X0] : number_number_of(int,X0) = X0,
inference(cnf_transformation,[],[f62]) ).
fof(f299,plain,
! [X0] : pls = times_times(int,pls,X0),
inference(cnf_transformation,[],[f102]) ).
fof(f302,plain,
! [X0,X1] : times_times(int,X0,X1) = times_times(int,X1,X0),
inference(cnf_transformation,[],[f63]) ).
fof(f305,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
inference(cnf_transformation,[],[f42]) ).
fof(f314,plain,
pls = zero_zero(int),
inference(forward_demodulation,[],[f262,f282]) ).
fof(f352,plain,
~ ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),zero_zero(int)),
inference(superposition,[],[f207,f257]) ).
fof(f353,plain,
~ ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),pls),
inference(forward_demodulation,[],[f352,f314]) ).
fof(f1133,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) = plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),
inference(forward_demodulation,[],[f243,f257]) ).
fof(f1134,plain,
plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(forward_demodulation,[],[f1133,f302]) ).
fof(f1135,plain,
plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,t,plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m))),
inference(forward_demodulation,[],[f1134,f257]) ).
fof(f1136,plain,
plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls))))))),
inference(forward_demodulation,[],[f1135,f302]) ).
fof(f1137,plain,
plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),
inference(forward_demodulation,[],[f1136,f282]) ).
fof(f1159,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))),
inference(forward_demodulation,[],[f305,f302]) ).
fof(f1160,plain,
ord_less(int,times_times(int,plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)),t),times_times(int,zero_zero(int),plus_plus(int,one_one(int),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m)))),
inference(forward_demodulation,[],[f1159,f257]) ).
fof(f1161,plain,
ord_less(int,times_times(int,plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls)))))),t),times_times(int,zero_zero(int),plus_plus(int,one_one(int),times_times(int,m,number_number_of(int,bit0(bit0(bit1(pls)))))))),
inference(forward_demodulation,[],[f1160,f302]) ).
fof(f1162,plain,
ord_less(int,times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),t),times_times(int,zero_zero(int),plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))))),
inference(forward_demodulation,[],[f1161,f282]) ).
fof(f1163,plain,
ord_less(int,times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),t),times_times(int,pls,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))))),
inference(forward_demodulation,[],[f1162,f314]) ).
fof(f1164,plain,
ord_less(int,times_times(int,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls))))),t),pls),
inference(forward_demodulation,[],[f1163,f299]) ).
fof(f1165,plain,
ord_less(int,times_times(int,t,plus_plus(int,one_one(int),times_times(int,m,bit0(bit0(bit1(pls)))))),pls),
inference(forward_demodulation,[],[f1164,f302]) ).
fof(f1166,plain,
ord_less(int,plus_plus(int,one_one(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),pls),
inference(forward_demodulation,[],[f1165,f1137]) ).
fof(f1167,plain,
$false,
inference(forward_subsumption_resolution,[],[f1166,f353]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n008.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 21:42:10 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.64/1.37 % (1629105)Detected formulas, will run a generic FOF schedule.
% 2.64/1.37 % (1629114)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2575535609:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.37 % (1629114)First to succeed.
% 2.64/1.37 % (1629114)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1629105"
% 2.64/1.37 % (1629112)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3035232436:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.37 % (1629110)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3408476992:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.37 % (1629111)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=551403490:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.37 % (1629113)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1689088378:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.37 % (1629116)dis-21_1_sil=8000:lcm=predicate:random_seed=2866035577:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.64/1.37 % (1629115)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3795106154:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.37 % (1629113)Instruction limit reached!
% 2.64/1.37 % (1629113)------------------------------
% 2.64/1.37 % (1629113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.37 % (1629113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.37 % (1629113)CaDiCaL version: 2.1.3
% 2.64/1.37 % (1629113)Termination reason: Instruction limit
% 2.64/1.37 % (1629113)Termination phase: Saturation
% 2.64/1.37 % (1629113)Time elapsed: 0.057 s
% 2.64/1.37 % (1629113)Peak memory usage: 89 MB
% 2.64/1.37 % (1629113)Instructions burned: 109 (million)
% 2.64/1.37 % (1629115)Also succeeded, but the first one will report.
% 2.64/1.37 % (1629116)Instruction limit reached!
% 2.64/1.37 % (1629116)------------------------------
% 2.64/1.37 % (1629116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.37 % (1629116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.37 % (1629116)CaDiCaL version: 2.1.3
% 2.64/1.37 % (1629116)Termination reason: Instruction limit
% 2.64/1.37 % (1629116)Termination phase: Saturation
% 2.64/1.37 % (1629116)Time elapsed: 0.076 s
% 2.64/1.37 % (1629116)Peak memory usage: 89 MB
% 2.64/1.37 % (1629116)Instructions burned: 129 (million)
% 2.64/1.37 % (1629114)Refutation found. Thanks to Tanya!
% 2.64/1.37 % SZS status Theorem for theBenchmark
% 2.64/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.37 % (1629114)------------------------------
% 2.64/1.37 % (1629114)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.37 % (1629114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.37 % (1629114)CaDiCaL version: 2.1.3
% 2.64/1.37 % (1629114)Termination reason: Refutation
% 2.64/1.37 % (1629114)Time elapsed: 0.018 s
% 2.64/1.37 % (1629114)Peak memory usage: 89 MB
% 2.64/1.37 % (1629114)Instructions burned: 51 (million)
% 2.64/1.37 % (1629114)------------------------------
% 2.64/1.37 % (1629114)------------------------------
% 2.64/1.37 % (1629105)Success in time 0.295 s
% 2.64/1.37 % Vampire exiting
%------------------------------------------------------------------------------